Question 124183: Please help me understand and accomplish the following problem:
The average weight of males in the freshman class of a certain college is 75.4 kg, with a standard deviation of 7.6 kg. Assume normal population. Interpret your result in each question.
a. What is the probability that the weight of a male freshman randomly selected from this population is greater than 83.5 kg? (believe P(x > 83.5 Kg))
b. What percent of the weights are less than 1.25 sigma or greather than 1.25 sigma?
c. What two weights separate the top 25% and bottom 25%, respectively, of the population?
d. Assume a sample of 35 weights is selected in random. What is the probability that the average of this sample is greater than 83.5? (believe need to apply Central Limit Theorem)
Appreciate your assistance in helping me complete this problem.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The average weight of males in the freshman class of a certain college is 75.4 kg, with a standard deviation of 7.6 kg. Assume normal population. Interpret your result in each question.
a. What is the probability that the weight of a male freshman randomly selected from this population is greater than 83.5 kg? (believe P(x > 83.5 Kg))
Find the z-score of 83.5; then your problem becomes
P(z>1.0657= 0.1433
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b. What percent of the weights are less than 1.25 sigma or greater than 1.25 sigma?
P(z< 1.25) = 0. 8943
P(z>1.25 ) = 0.10565
Comment: If your stated problem was an OR statement the answer is 100%
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c. What two weights separate the top 25% and bottom 25%, respectively, of the population?
Find the z-value associated with 25%: z=-0.6745 and z=+0.6745
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Convert to a Raw or x-score:
z(x) = (x-mu)/sigma
-0.6745 = (x-75.4)/7.6
x = 70.27
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+0.6745 = (x-75.4)/7.6
x= 80.526
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d. Assume a sample of 35 weights is selected in random. What is the probability that the average of this sample is greater than 83.5?
Find the z-score:
z(83.5)=(83.5-75.4)/[7.6/sqrt(35)] = 6.305
P(z>6.305) is approximately zero
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Cheers,
Stan H.
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